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A Comparative Study of Various Model-Theoretic Treatments of Negation: A History of Formal Negation

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What is Negation?

Part of the book series: Applied Logic Series ((APLS,volume 13))

Abstract

There are different treatments of the semantics of negation in non-classical logics, the most familiar of which is probably the Kripke definition of negation for intuitionistic logic. In two recent papers I have explored generalizations of Goldblatt’s semantics for negation in orthologic (which uses the perp relation), and related these to the Kripke definition of negation for intuitonistic logic, and to the definition of De Morgan negation in relevance logic (which standardly uses the ‘star operator’ *). The present paper in part surveys this earlier work, but the main focus is to connect the alternative four-valued semantics of De Morgan negation (using ‘overdetermined’ and ‘underdetermined’ truth values) to the star semantics (and hence indirectly to the perp semantics). This connection is based on semi-published work of mine from the 1960’s.

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Authors and Affiliations

  1. Indiana University, USA

    J. Michael Dunn

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  1. J. Michael Dunn
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Editors and Affiliations

  1. King’s College, London, UK

    Dov M. Gabbay

  2. University of Leipzig, Leipzig, Germany

    Heinrich Wansing

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Dunn, J.M. (1999). A Comparative Study of Various Model-Theoretic Treatments of Negation: A History of Formal Negation. In: Gabbay, D.M., Wansing, H. (eds) What is Negation?. Applied Logic Series, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9309-0_2

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  • DOI: https://doi.org/10.1007/978-94-015-9309-0_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5169-1

  • Online ISBN: 978-94-015-9309-0

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